1. Since $m \parallel \beta$, $m \subset \alpha$, and $\alpha \cap \beta = n$,
by the property of a line being parallel to a plane, we know: $m \parallel n$. Therefore, proposition 1 is correct.
2. Since $n \parallel \beta$ and $\alpha \parallel \beta$, then $n \parallel \alpha$.
Since $m \perp \alpha$, then $m \perp n$. Therefore, proposition 2 is correct.
3. Since $m \perp \alpha$, $\alpha \parallel \beta$,
then $m \perp \beta$.
Since $n \parallel \beta$,
then $m \perp n$. Therefore, proposition 3 is correct.
4. Since $m \perp \alpha$, $n \perp \beta$ and $\alpha \perp \beta$,
then $m \perp n$. Therefore, proposition 4 is correct.

Therefore, the correct choice is $\boxed{\text{D}}$.